Topics in economic theory (EC219):
coalitional games

Graduate program in economics, Brown University, Academic year 1999/2000

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General Description

Game theory is a branch of mathematics which is used in modelling situations in which players with conflicting interests interact. Coalitional Games are games in which the possibilities of the players are described by the available resources of different groups (coalitions) of players.

The course topics in economic theory (EC219) will discuss the major principles of this branch of game theory, and some of its applications to economics as well as to other fields of social science. In the first part of the course we shall study the core of transferable utility games. Among other things, the relations between the core and price-equilibrium will receive a considerable attention.

The second part of the course will concentrate on the axiomatic approach to solution concepts. We shall discuss the major developments of the recent fifteen years or so, highlighting the centrality of the consistency axiom, and of the core as a solution concept. Within the axiomatic approach we will also discuss the prekernel and the Shapley value, and some of their applications in economics, political science, and Jewish law.

In the third part of the course, we will discus general coalitional games, which include the Nash bargaining problem and non-transferable utility games, among other models. In this part of the course we will check to what extent results of transferable utility games can be generalized.

Part 1: The core of transferable utility games

Part 2: The axiomatic approach to solution concepts

Part 3: General coalitional games

Bibliography

We shall not follow a particular textbook. Most of the first part and some of the third part are covered by the textbooks mentioned below, but most of the second part is not covered by textbooks. Thus, in the second part journal articles will have a larger role.

Textbooks

Articles